The English top flight needed just one win from its clubs in any of the three European competitions to secure one of two extra berths - on top of the four granted to the top four in the table - awarded to the highest-ranked countries in the UEFA coefficient ranking.
In this system, teams earn two points for a win and one for a draw, adding up all the points obtained by each club and dividing by the number of clubs from that league participating in Europe. Bonus points are also on offer depending on progression in this season's European competitions.
England could have up to seven teams in the upcoming Champions League if Aston Villa win this year's edition without qualifying through the Premier League table, and if either Manchester United or Tottenham Hotspur are crowned in the Europa League.
Spain leads the race for the second additional place, with Italy and Germany trailing behind with the top German clubs unable to reach top spot in the rankings.
Premier League leaders Liverpool and second-placed Arsenal look set to claim two of the five available berths, while Nottingham Forest hold a strong third position.
Chelsea, Newcastle United, Manchester City, Aston Villa, Brighton & Hove Albion, and 10th-place Bournemouth remain within eight points of each other.